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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 1560a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1560.b4 | 1560a1 | \([0, -1, 0, 84, 180]\) | \(253012016/219375\) | \(-56160000\) | \([2]\) | \(384\) | \(0.17451\) | \(\Gamma_0(N)\)-optimal |
| 1560.b3 | 1560a2 | \([0, -1, 0, -416, 1980]\) | \(7793764996/3080025\) | \(3153945600\) | \([2, 2]\) | \(768\) | \(0.52108\) | |
| 1560.b2 | 1560a3 | \([0, -1, 0, -3016, -61460]\) | \(1481943889298/34543665\) | \(70745425920\) | \([2]\) | \(1536\) | \(0.86766\) | |
| 1560.b1 | 1560a4 | \([0, -1, 0, -5816, 172620]\) | \(10625310339698/3855735\) | \(7896545280\) | \([2]\) | \(1536\) | \(0.86766\) |
Rank
sage: E.rank()
The elliptic curves in class 1560a have rank \(0\).
Complex multiplication
The elliptic curves in class 1560a do not have complex multiplication.Modular form 1560.2.a.a
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
